I'm really struggling trying to understand what formulas to use for the following:
A satellite orbits the earth with a radius of 7000 km. (a) what is the acceleration of gravity at this distance? (b) what is the velocity of the satellite? (c) how long does it take the satellite to make one orbit.
Can someone help please?
answered
Sure! I can help you understand how to solve these problems step by step.
(a) To find the acceleration of gravity at a given distance from the center of the Earth, we can use the formula for gravitational acceleration:
g = G * (M / r^2)
Where:
- g is the acceleration of gravity
- G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
- M is the mass of the Earth (approximately 5.972 × 10^24 kg)
- r is the distance from the center of the Earth to the satellite's orbit (7000 km = 7000000 m)
Plugging the values into the formula, we can calculate the acceleration of gravity at this distance.
(b) To find the velocity of the satellite, we can use the formula for the orbital velocity:
v = √(G * M / r)
Where:
- v is the velocity of the satellite
- G is the gravitational constant
- M is the mass of the Earth
- r is the distance from the center of the Earth to the satellite's orbit
By substituting the given values into this formula, we can calculate the velocity of the satellite.
(c) The time it takes for the satellite to complete one orbit can be determined using the formula for orbital period:
T = 2π * √(r^3 / (G * M))
Where:
- T is the orbital period of the satellite
- G is the gravitational constant
- M is the mass of the Earth
- r is the distance from the center of the Earth to the satellite's orbit
By substituting the known values into this formula, we can calculate the time it takes for the satellite to make one complete orbit.
I hope this helps you understand how to approach these problems! Let me know if you have any further questions.